Distributed Binary Consensus in Networks with Disturbances

This article evaluates convergence rates of binary majority consensus algorithms in networks with different types of disturbances and studies the potential capacity of randomization to foster convergence. Simulation results show that (a) additive noise, topology randomness, and stochastic message loss may improve the convergence rate; (b) presence of faulty nodes degrades the convergence rate; and (c) explicit randomization of consensus algorithms can be exploited to improve the convergence rate. Watts-Strogatz and Waxman graphs are used as underlying network topologies. A consensus algorithm is proposed that exchanges state information with dynamically randomly selected neighbors and, through this randomization, achieves almost sure convergence in some scenarios.